If the previous provider didn't mention that they use WordPress, then you may want to request the admin access from them.

If they refuse to hand it over, be sure that you've access to your hosting server (especially MySQL). However, if the provider is also hosting for you and never in your life have you requested the access, things become difficult.

Only thing you can do in this case is to read the project agreement and determine whether they stated that access will not be granted to you. Or, if there's a small print that goes "any other request is ignored unless specified"

Anyway.. if the provider has a sense of professionalism, they should provide you (client) access to what you need.